How do I save an object in a blender file separate from the blend file?
If you are looking to make separate .blend files of particular objects you will use later on in different scenes, there are a few things you must consider.

Actually Making Separate .blends:

If you have an object in a scene that you want to keep for later use but you don't want it in that particular scene, you can simply press ctrl+c in Object Mode with that object selected and it will bring up a menu and it will ask you to copy to buffer... Select that.

Now open up a brand new blender and delete everything in the new blender scene except the lamp and camera. (that is if you need to)

Press ctrl+v to paste the object that you copied to buffer from the other blend and it will appear with all the file paths and textures just like in the original blend. If you do not want to have the object in its original .blend file (not the one you copied to) you can delete it because you copied it to a new file.

Always save your progress. 

The Things You Need to Consider:

When making separate .blends for individual objects you computer gets full fast. I have had experience. When you computer is full, blender becomes very slow. I have found that putting packs of objects in a .blend file that are related is very helpful and you can find objects you are looking for faster. 

EX: You have household items like plates and you have different models for each plate. Put them all in the same .blend but move each different model to different layers. 

Another way to have them separate in the same .blend file is to have the objects in separate groups, with this method you will need to have everything in the .blend file visible to the camera because when linking object groups into a new scene it can get frustrating when you try to render things and cannot see them. You can learn about grouping, linking and appending here https://www.youtube.com/watch?v=iOgOKp7fGko

Also when making separate .blends for an object/objects you need to think about your file structure because when you build up a repository of .blends it can get really confusing when you are trying to find something. Good, organized file structure is so much better than having files all over your computer.

An example of good file structure can be found here http://artstorm.net/journal/2011/08/filmmaking-file-structure/

I hoped this helped in some way.